How to have a even thickness around the mesh
The only way is to split corner edge. You can use Edge Split modifier if you don't care about overlapping geometry.

Or try to set Even and Offset minus 1 instead, so it looks a bit nicer from some angle. But the corner will always fail.

Solidify generates a copy of each vertex with offset in face normal direction. In your case the problem is RIM. Generated faces on sides are pointed in oposite direction. Blender tries calculate average connection that results in a twist.
By other words - the result you expect require additional geometry, it is more than  - copy vertex and offset. It meams you'r asking modifier to do more than was designed.